The Breuil-Mézard conjecture is concerned with the special fibre of
\(R^{\lambda ,{\rm t}}_{\overline{\rho }}\)  but, of course, obtaining a complete
description of the ring \(R^{\lambda ,{\rm t}}_{\overline{\rho }}\)  has also interest
for its own. For example, explicit presentations of some
\(R^{\lambda ,{\rm t}}_{\overline{\rho }}\)  have been used
by Emerton, Gee and Savitt [1]} to prove important conjectures
stated by Breuil in [2]} about lattices in the cohomology of
Shimura curves.
In this subsection, we outline the standard strategy that is used
to approach \(R^{\lambda ,{\rm t}}_{\overline{\rho }}\)  and report on the results
of some explicit computations.
